Heating and driving non-inductive current in plasmas by means of Radio Frequency (RF) waves in the range of the Lower Hybrid (LH) frequencies is important for Steady State (SS) operation in fusion. The penetration of LH waves at higher densities has been recently reviewed in order to assess the Lower Hybrid Current Drive (LHCD) performance in conditions as close as possible to the ITER SS scenario. The analysis of various experiments performed on C-Mod, FTU, Tore Supra and JET indicate a degradation of the Current Drive (CD) efficiency when the plasma density is increased, while at the same time the LH wave absorption shifts to the plasma periphery. JET pulses in H-mode confirm this trend and in addition it was found that the accessibility condition is not the main parameter to explain the reduction in the CD efficiency. This paper discusses further the LH deposition in H-mode plasmas and in particular it shows that lower pedestal density and higher temperature are beneficial regarding the LH wave penetration. The investigation presented here is based on the analysis of the Electron Cyclotron Emission (ECE) spectra in plasmas with fast electrons generated by LH waves. The study includes the numerical calculation of the ECE intensity and a comparison with experimental profiles in the plasma periphery for optically thin frequencies.